EDAV Project 2 - PCA Analysis
Team Noname
March 7, 2016
Principal component analysis on the floods in the UK during 1990
We decided to subset the data and focus our attention in 5 flood events that occurred in the United Kingdom during 1990. We came up with these events after slicing the Global Floods data over time and generating an animation as allowed us to perfectly tackle big and isolated flood events over time.
## Extraction of phi data
uk.floods = global.flood[c(3837,3845,3856,3924,3930),]Transforming the data
Once the entries for the UK floods in 1990 have been located in the NOAA daily phi data, global flood records dates are transformed so that the two tables can be correctly related
uk.floods$Began <- as.numeric(as.POSIXct(as.Date(uk.floods$Began, "%d-%b-%y"), origin="1948-01-01")) %/% (24*60*60)
uk.floods$Ended <- as.numeric(as.POSIXct(as.Date(uk.floods$Ended, "%d-%b-%y"), origin="1948-01-01")) %/% (24*60*60)
uk.floods[,c("Began","Ended")]## Began Ended
## 3837 7663 7666
## 3845 7605 7607
## 3856 7583 7584
## 3924 7361 7363
## 3930 7330 7345Using these intervals we proceeded to split the phi data into:
- All longitudes
- Latitudes from 45ºN to 60ºN
- Days ranging from 30 days before the start date to 30 days after the end date
uk.floods.x <- which(daily.geopot.height$X > -1)
uk.floods.y <- which(daily.geopot.height$Y >= 45 & daily.geopot.height$Y <= 60)
interval <- function(x,y) {
c(x - 30, y + 30)
}
uk.floods.t.1 <- interval(7663,7666)
uk.floods.t.2 <- interval(7605,7607)
uk.floods.t.3 <- interval(7583,7584)
uk.floods.t.4 <- interval(7361,7363)
uk.floods.t.5 <- interval(7330,7345)
generate_data <- function(x,y,range){
dims <- c(length(x) * length(y), range[2]-range[1]+1)
size <- length(x) * length(y) * (range[2]-range[1]+1)
data <- array(1:size, dim=dims)
j <- 1
for (i in range[1]:range[2]){
data[,j] <- as.vector(t(daily.geopot.height$phi[x, y, i]))
j <- j + 1
}
return(data)
}
uk.floods.phi.1 <- generate_data(uk.floods.x, uk.floods.y, uk.floods.t.1)
uk.floods.phi.2 <- generate_data(uk.floods.x, uk.floods.y, uk.floods.t.2)
uk.floods.phi.3 <- generate_data(uk.floods.x, uk.floods.y, uk.floods.t.3)
uk.floods.phi.4 <- generate_data(uk.floods.x, uk.floods.y, uk.floods.t.4)
uk.floods.phi.5 <- generate_data(uk.floods.x, uk.floods.y, uk.floods.t.5)Once we have the slices for each flood event, we ran PCA on them:
uk.floods.pca.1 <- princomp(uk.floods.phi.1, cor = TRUE, scores = TRUE)
uk.floods.pca.2 <- princomp(uk.floods.phi.2, cor = TRUE, scores = TRUE)
uk.floods.pca.3 <- princomp(uk.floods.phi.3, cor = TRUE, scores = TRUE)
uk.floods.pca.4 <- princomp(uk.floods.phi.4, cor = TRUE, scores = TRUE)
uk.floods.pca.5 <- princomp(uk.floods.phi.5, cor = TRUE, scores = TRUE)
summary(uk.floods.pca.1)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 5.5428126 2.9515918 2.48046518 1.82251017
## Proportion of Variance 0.4800433 0.1361233 0.09613605 0.05189911
## Cumulative Proportion 0.4800433 0.6161666 0.71230270 0.76420181
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 1.72472263 1.34675032 1.2858591 1.16932601
## Proportion of Variance 0.04647919 0.02833963 0.0258349 0.02136443
## Cumulative Proportion 0.81068100 0.83902064 0.8648555 0.88621996
## Comp.9 Comp.10 Comp.11 Comp.12
## Standard deviation 1.03778324 0.97687798 0.88555546 0.83398758
## Proportion of Variance 0.01682803 0.01491079 0.01225326 0.01086774
## Cumulative Proportion 0.90304799 0.91795878 0.93021204 0.94107978
## Comp.13 Comp.14 Comp.15 Comp.16
## Standard deviation 0.793749748 0.626746517 0.573708158 0.524433517
## Proportion of Variance 0.009844354 0.006137675 0.005142829 0.004297352
## Cumulative Proportion 0.950924135 0.957061810 0.962204639 0.966501990
## Comp.17 Comp.18 Comp.19 Comp.20
## Standard deviation 0.494338471 0.467170644 0.435385818 0.412190488
## Proportion of Variance 0.003818289 0.003410131 0.002961888 0.002654703
## Cumulative Proportion 0.970320280 0.973730411 0.976692299 0.979347002
## Comp.21 Comp.22 Comp.23 Comp.24
## Standard deviation 0.3812821 0.337125897 0.333472773 0.307186937
## Proportion of Variance 0.0022715 0.001775842 0.001737564 0.001474435
## Cumulative Proportion 0.9816185 0.983394344 0.985131908 0.986606342
## Comp.25 Comp.26 Comp.27 Comp.28
## Standard deviation 0.299800148 0.279972984 0.263207732 0.2478024447
## Proportion of Variance 0.001404377 0.001224764 0.001082474 0.0009594696
## Cumulative Proportion 0.988010719 0.989235483 0.990317957 0.9912774261
## Comp.29 Comp.30 Comp.31 Comp.32
## Standard deviation 0.2354442700 0.2269615887 0.2136297658 0.2038270777
## Proportion of Variance 0.0008661563 0.0008048682 0.0007130887 0.0006491481
## Cumulative Proportion 0.9921435824 0.9929484506 0.9936615393 0.9943106874
## Comp.33 Comp.34 Comp.35 Comp.36
## Standard deviation 0.1812106128 0.1779718986 0.1686612915 0.1664002714
## Proportion of Variance 0.0005130826 0.0004949062 0.0004444786 0.0004326414
## Cumulative Proportion 0.9948237700 0.9953186762 0.9957631548 0.9961957962
## Comp.37 Comp.38 Comp.39 Comp.40
## Standard deviation 0.1540856670 0.149071141 0.1392531748 0.1299883254
## Proportion of Variance 0.0003709749 0.000347222 0.0003029914 0.0002640151
## Cumulative Proportion 0.9965667711 0.996913993 0.9972169844 0.9974809995
## Comp.41 Comp.42 Comp.43 Comp.44
## Standard deviation 0.1269949048 0.1227905374 0.1148577325 0.1111628327
## Proportion of Variance 0.0002519954 0.0002355862 0.0002061297 0.0001930809
## Cumulative Proportion 0.9977329949 0.9979685811 0.9981747107 0.9983677916
## Comp.45 Comp.46 Comp.47 Comp.48
## Standard deviation 0.1058692382 0.1026929396 0.0967983997 0.0959115396
## Proportion of Variance 0.0001751296 0.0001647787 0.0001464052 0.0001437347
## Cumulative Proportion 0.9985429212 0.9987077000 0.9988541051 0.9989978399
## Comp.49 Comp.50 Comp.51 Comp.52
## Standard deviation 0.086068640 0.0851839751 7.896836e-02 7.612013e-02
## Proportion of Variance 0.000115747 0.0001133798 9.743754e-05 9.053553e-05
## Cumulative Proportion 0.999113587 0.9992269667 9.993244e-01 9.994149e-01
## Comp.53 Comp.54 Comp.55 Comp.56
## Standard deviation 7.224699e-02 6.711442e-02 6.429725e-02 6.041894e-02
## Proportion of Variance 8.155668e-05 7.038039e-05 6.459587e-05 5.703826e-05
## Cumulative Proportion 9.994965e-01 9.995669e-01 9.996315e-01 9.996885e-01
## Comp.57 Comp.58 Comp.59 Comp.60
## Standard deviation 5.883503e-02 5.714398e-02 5.446225e-02 5.186803e-02
## Proportion of Variance 5.408688e-05 5.102241e-05 4.634588e-05 4.203583e-05
## Cumulative Proportion 9.997426e-01 9.997936e-01 9.998400e-01 9.998820e-01
## Comp.61 Comp.62 Comp.63 Comp.64
## Standard deviation 4.943895e-02 4.550653e-02 0.0405321416 3.733581e-02
## Proportion of Variance 3.819078e-05 3.235694e-05 0.0000256696 2.178066e-05
## Cumulative Proportion 9.999202e-01 9.999525e-01 0.9999782193 1.000000e+00plot(uk.floods.pca.1,type = "l")
biplot(uk.floods.pca.1)
summary(uk.floods.pca.2)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 5.7914986 2.5766337 2.03315372 1.68693923
## Proportion of Variance 0.5324041 0.1053816 0.06561451 0.04517086
## Cumulative Proportion 0.5324041 0.6377857 0.70340018 0.74857103
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 1.55516019 1.45535431 1.31504182 1.18106522
## Proportion of Variance 0.03838926 0.03361994 0.02744976 0.02214151
## Cumulative Proportion 0.78696029 0.82058023 0.84802999 0.87017150
## Comp.9 Comp.10 Comp.11 Comp.12
## Standard deviation 1.13926441 1.10797992 0.9446200 0.8662195
## Proportion of Variance 0.02060196 0.01948602 0.0141636 0.0119101
## Cumulative Proportion 0.89077346 0.91025948 0.9244231 0.9363332
## Comp.13 Comp.14 Comp.15 Comp.16
## Standard deviation 0.672704884 0.647042660 0.599396769 0.56264156
## Proportion of Variance 0.007183045 0.006645464 0.005702801 0.00502485
## Cumulative Proportion 0.943516229 0.950161693 0.955864494 0.96088934
## Comp.17 Comp.18 Comp.19 Comp.20
## Standard deviation 0.534804998 0.509096026 0.479531260 0.434310933
## Proportion of Variance 0.004539943 0.004113949 0.003650004 0.002994063
## Cumulative Proportion 0.965429286 0.969543235 0.973193239 0.976187302
## Comp.21 Comp.22 Comp.23 Comp.24
## Standard deviation 0.429494503 0.399321329 0.385714730 0.344945671
## Proportion of Variance 0.002928024 0.002531072 0.002361521 0.001888691
## Cumulative Proportion 0.979115326 0.981646398 0.984007920 0.985896610
## Comp.25 Comp.26 Comp.27 Comp.28
## Standard deviation 0.307808131 0.287796038 0.271133216 0.268433130
## Proportion of Variance 0.001503902 0.001314707 0.001166877 0.001143752
## Cumulative Proportion 0.987400513 0.988715220 0.989882096 0.991025848
## Comp.29 Comp.30 Comp.31 Comp.32
## Standard deviation 0.244780718 0.2378794578 0.220259586 0.2072855330
## Proportion of Variance 0.000951073 0.0008982006 0.000770068 0.0006820205
## Cumulative Proportion 0.991976921 0.9928751215 0.993645190 0.9943272100
## Comp.33 Comp.34 Comp.35 Comp.36
## Standard deviation 0.1849073918 0.1727819699 0.1711256422 0.1551283133
## Proportion of Variance 0.0005427102 0.0004738668 0.0004648252 0.0003819809
## Cumulative Proportion 0.9948699203 0.9953437871 0.9958086122 0.9961905931
## Comp.37 Comp.38 Comp.39 Comp.40
## Standard deviation 0.1514736283 0.1457754718 0.1425389311 0.1362243222
## Proportion of Variance 0.0003641946 0.0003373093 0.0003224976 0.0002945566
## Cumulative Proportion 0.9965547877 0.9968920970 0.9972145946 0.9975091512
## Comp.41 Comp.42 Comp.43 Comp.44
## Standard deviation 0.1271351193 0.1256545841 0.1179316034 0.1115743787
## Proportion of Variance 0.0002565609 0.0002506202 0.0002207597 0.0001976007
## Cumulative Proportion 0.9977657121 0.9980163324 0.9982370921 0.9984346928
## Comp.45 Comp.46 Comp.47 Comp.48
## Standard deviation 0.106734975 0.1004459134 0.0967299238 0.0952466223
## Proportion of Variance 0.000180831 0.0001601489 0.0001485187 0.0001439987
## Cumulative Proportion 0.998615524 0.9987756727 0.9989241914 0.9990681901
## Comp.49 Comp.50 Comp.51 Comp.52
## Standard deviation 0.0880635999 0.0838067008 0.0803390640 7.748467e-02
## Proportion of Variance 0.0001230984 0.0001114851 0.0001024502 9.529959e-05
## Cumulative Proportion 0.9991912885 0.9993027736 0.9994052239 9.995005e-01
## Comp.53 Comp.54 Comp.55 Comp.56
## Standard deviation 6.873348e-02 0.063771771 5.972640e-02 5.899985e-02
## Proportion of Variance 7.498875e-05 0.000064553 5.662291e-05 5.525368e-05
## Cumulative Proportion 9.995755e-01 0.999640065 9.996967e-01 9.997519e-01
## Comp.57 Comp.58 Comp.59 Comp.60
## Standard deviation 5.587238e-02 5.239672e-02 5.083849e-02 4.678487e-02
## Proportion of Variance 4.955116e-05 4.357803e-05 4.102463e-05 3.474325e-05
## Cumulative Proportion 9.998015e-01 9.998451e-01 9.998861e-01 9.999208e-01
## Comp.61 Comp.62 Comp.63
## Standard deviation 4.334473e-02 0.0419344749 3.674080e-02
## Proportion of Variance 2.982168e-05 0.0000279127 2.142677e-05
## Cumulative Proportion 9.999507e-01 0.9999785732 1.000000e+00plot(uk.floods.pca.2,type = "l")
biplot(uk.floods.pca.2)
summary(uk.floods.pca.3)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 5.2938692 2.6580452 2.25340883 2.02650892
## Proportion of Variance 0.4520169 0.1139549 0.08190083 0.06623772
## Cumulative Proportion 0.4520169 0.5659719 0.64787268 0.71411040
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 1.67438048 1.56755744 1.37654757 1.28550769
## Proportion of Variance 0.04521855 0.03963284 0.03056263 0.02665371
## Cumulative Proportion 0.75932895 0.79896179 0.82952442 0.85617813
## Comp.9 Comp.10 Comp.11 Comp.12
## Standard deviation 1.20545766 1.15035126 0.93005447 0.85195612
## Proportion of Variance 0.02343755 0.02134368 0.01395163 0.01170692
## Cumulative Proportion 0.87961568 0.90095936 0.91491100 0.92661792
## Comp.13 Comp.14 Comp.15 Comp.16
## Standard deviation 0.741437580 0.679919411 0.651188725 0.644603034
## Proportion of Variance 0.008866608 0.007456297 0.006839464 0.006701824
## Cumulative Proportion 0.935484528 0.942940824 0.949780288 0.956482112
## Comp.17 Comp.18 Comp.19 Comp.20
## Standard deviation 0.584597568 0.538380162 0.499047712 0.481103591
## Proportion of Variance 0.005512166 0.004675052 0.004016913 0.003733237
## Cumulative Proportion 0.961994278 0.966669330 0.970686243 0.974419480
## Comp.21 Comp.22 Comp.23 Comp.24
## Standard deviation 0.423923375 0.409626402 0.362209281 0.35062511
## Proportion of Variance 0.002898565 0.002706351 0.002116057 0.00198287
## Cumulative Proportion 0.977318045 0.980024396 0.982140454 0.98412332
## Comp.25 Comp.26 Comp.27 Comp.28
## Standard deviation 0.314139557 0.298218180 0.292358284 0.275495982
## Proportion of Variance 0.001591672 0.001434421 0.001378603 0.001224162
## Cumulative Proportion 0.985714996 0.987149417 0.988528019 0.989752181
## Comp.29 Comp.30 Comp.31 Comp.32
## Standard deviation 0.265092498 0.252704834 0.2328552340 0.2261129049
## Proportion of Variance 0.001133452 0.001029996 0.0008745413 0.0008246298
## Cumulative Proportion 0.990885633 0.991915629 0.9927901704 0.9936148002
## Comp.33 Comp.34 Comp.35 Comp.36
## Standard deviation 0.1942658611 0.1795607865 0.1724554016 0.1658891648
## Proportion of Variance 0.0006086972 0.0005200335 0.0004796914 0.0004438583
## Cumulative Proportion 0.9942234973 0.9947435308 0.9952232222 0.9956670805
## Comp.37 Comp.38 Comp.39 Comp.40
## Standard deviation 0.1607241976 0.1572177236 0.1510054183 0.1465683292
## Proportion of Variance 0.0004166495 0.0003986679 0.0003677845 0.0003464883
## Cumulative Proportion 0.9960837300 0.9964823979 0.9968501824 0.9971966707
## Comp.41 Comp.42 Comp.43 Comp.44
## Standard deviation 0.1418071591 0.1365331380 0.1246291368 0.1140609925
## Proportion of Variance 0.0003243431 0.0003006661 0.0002505229 0.0002098373
## Cumulative Proportion 0.9975210138 0.9978216799 0.9980722028 0.9982820400
## Comp.45 Comp.46 Comp.47 Comp.48
## Standard deviation 0.1071221862 0.1023465376 0.0981430711 0.0961575403
## Proportion of Variance 0.0001850833 0.0001689486 0.0001553558 0.0001491334
## Cumulative Proportion 0.9984671233 0.9986360719 0.9987914278 0.9989405612
## Comp.49 Comp.50 Comp.51 Comp.52
## Standard deviation 0.0936399679 0.0864824739 0.08435851 0.0810879961
## Proportion of Variance 0.0001414265 0.0001206326 0.00011478 0.0001060526
## Cumulative Proportion 0.9990819877 0.9992026203 0.99931740 0.9994234529
## Comp.53 Comp.54 Comp.55 Comp.56
## Standard deviation 0.0760095490 7.571987e-02 7.126708e-02 0.0644860568
## Proportion of Variance 0.0000931847 9.247579e-05 8.191931e-05 0.0000670718
## Cumulative Proportion 0.9995166376 9.996091e-01 9.996910e-01 0.9997581045
## Comp.57 Comp.58 Comp.59 Comp.60
## Standard deviation 6.257980e-02 5.481935e-02 4.892527e-02 4.664822e-02
## Proportion of Variance 6.316501e-05 4.847035e-05 3.860778e-05 3.509768e-05
## Cumulative Proportion 9.998213e-01 9.998697e-01 9.999083e-01 9.999434e-01
## Comp.61 Comp.62
## Standard deviation 4.245669e-02 0.041277379
## Proportion of Variance 2.907372e-05 0.000027481
## Cumulative Proportion 9.999725e-01 1.000000000plot(uk.floods.pca.3,type = "l")
biplot(uk.floods.pca.3)
summary(uk.floods.pca.4)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 4.7869281 3.1080861 2.7410716 2.19377798 1.98965968
## Proportion of Variance 0.3637251 0.1533365 0.1192615 0.07639146 0.06283723
## Cumulative Proportion 0.3637251 0.5170616 0.6363231 0.71271453 0.77555176
## Comp.6 Comp.7 Comp.8 Comp.9
## Standard deviation 1.69507822 1.56778212 1.16863526 1.09341065
## Proportion of Variance 0.04560778 0.03901493 0.02167791 0.01897693
## Cumulative Proportion 0.82115954 0.86017447 0.88185238 0.90082932
## Comp.10 Comp.11 Comp.12 Comp.13
## Standard deviation 0.97608289 0.86254198 0.770816241 0.71321559
## Proportion of Variance 0.01512282 0.01180919 0.009431074 0.00807423
## Cumulative Proportion 0.91595214 0.92776132 0.937192399 0.94526663
## Comp.14 Comp.15 Comp.16 Comp.17
## Standard deviation 0.662687770 0.622374403 0.593903068 0.538138908
## Proportion of Variance 0.006970716 0.006148411 0.005598744 0.004596722
## Cumulative Proportion 0.952237344 0.958385756 0.963984499 0.968581221
## Comp.18 Comp.19 Comp.20 Comp.21
## Standard deviation 0.523684033 0.420935441 0.414724004 0.389568484
## Proportion of Variance 0.004353095 0.002812486 0.002730095 0.002408946
## Cumulative Proportion 0.972934316 0.975746802 0.978476898 0.980885844
## Comp.22 Comp.23 Comp.24 Comp.25
## Standard deviation 0.351435583 0.334014483 0.31105329 0.303903045
## Proportion of Variance 0.001960428 0.001770884 0.00153578 0.001465985
## Cumulative Proportion 0.982846272 0.984617156 0.98615294 0.987618921
## Comp.26 Comp.27 Comp.28 Comp.29
## Standard deviation 0.288710201 0.268304049 0.2473686122 0.2428001108
## Proportion of Variance 0.001323073 0.001142652 0.0009712894 0.0009357443
## Cumulative Proportion 0.988941993 0.990084645 0.9910559346 0.9919916790
## Comp.30 Comp.31 Comp.32 Comp.33
## Standard deviation 0.2227578186 0.2056951515 0.2035116813 0.1896102211
## Proportion of Variance 0.0007876356 0.0006715952 0.0006574128 0.0005706672
## Cumulative Proportion 0.9927793146 0.9934509098 0.9941083226 0.9946789898
## Comp.34 Comp.35 Comp.36 Comp.37
## Standard deviation 0.1788091235 0.1732990919 0.1635975222 0.1578360999
## Proportion of Variance 0.0005075032 0.0004767075 0.0004248278 0.0003954323
## Cumulative Proportion 0.9951864930 0.9956632006 0.9960880283 0.9964834606
## Comp.38 Comp.39 Comp.40 Comp.41
## Standard deviation 0.1510721125 0.1353475422 0.1338550089 0.1255108249
## Proportion of Variance 0.0003622664 0.0002907771 0.0002843994 0.0002500471
## Cumulative Proportion 0.9968457270 0.9971365041 0.9974209035 0.9976709506
## Comp.42 Comp.43 Comp.44 Comp.45
## Standard deviation 0.1193761716 0.1162381718 0.1150479880 0.1066346176
## Proportion of Variance 0.0002262011 0.0002144653 0.0002100959 0.0001804911
## Cumulative Proportion 0.9978971518 0.9981116170 0.9983217129 0.9985022040
## Comp.46 Comp.47 Comp.48 Comp.49
## Standard deviation 0.1006978758 0.0988381641 0.0937515086 0.091193835
## Proportion of Variance 0.0001609534 0.0001550632 0.0001395134 0.000132005
## Cumulative Proportion 0.9986631574 0.9988182206 0.9989577340 0.999089739
## Comp.50 Comp.51 Comp.52 Comp.53
## Standard deviation 0.0874813180 0.0824329058 0.07918977 7.687006e-02
## Proportion of Variance 0.0001214759 0.0001078601 0.00009954 9.379376e-05
## Cumulative Proportion 0.9992112149 0.9993190750 0.99941862 9.995124e-01
## Comp.54 Comp.55 Comp.56 Comp.57
## Standard deviation 6.894398e-02 6.681377e-02 6.445607e-02 6.138645e-02
## Proportion of Variance 7.544878e-05 7.085841e-05 6.594579e-05 5.981422e-05
## Cumulative Proportion 9.995879e-01 9.996587e-01 9.997247e-01 9.997845e-01
## Comp.58 Comp.59 Comp.60 Comp.61
## Standard deviation 5.706758e-02 5.158880e-02 4.604085e-02 4.480615e-02
## Proportion of Variance 5.169378e-05 4.224451e-05 3.364698e-05 3.186652e-05
## Cumulative Proportion 9.998362e-01 9.998784e-01 9.999121e-01 9.999439e-01
## Comp.62 Comp.63
## Standard deviation 4.385092e-02 4.012042e-02
## Proportion of Variance 3.052228e-05 2.554997e-05
## Cumulative Proportion 9.999745e-01 1.000000e+00plot(uk.floods.pca.4,type = "l")
biplot(uk.floods.pca.4)
summary(uk.floods.pca.5)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 5.5246005 3.3717505 2.8793219 2.34074667 2.07905339
## Proportion of Variance 0.4015949 0.1495882 0.1090855 0.07209336 0.05687451
## Cumulative Proportion 0.4015949 0.5511831 0.6602685 0.73236187 0.78923639
## Comp.6 Comp.7 Comp.8 Comp.9
## Standard deviation 1.65068186 1.46332986 1.30396168 1.20054850
## Proportion of Variance 0.03585198 0.02817545 0.02237258 0.01896469
## Cumulative Proportion 0.82508837 0.85326382 0.87563640 0.89460109
## Comp.10 Comp.11 Comp.12 Comp.13
## Standard deviation 1.0777961 0.93388575 0.88641449 0.84324408
## Proportion of Variance 0.0152848 0.01147556 0.01033856 0.00935606
## Cumulative Proportion 0.9098859 0.92136145 0.93170001 0.94105607
## Comp.14 Comp.15 Comp.16 Comp.17
## Standard deviation 0.718511388 0.676440212 0.658449589 0.590156398
## Proportion of Variance 0.006792877 0.006020676 0.005704682 0.004582692
## Cumulative Proportion 0.947848948 0.953869624 0.959574306 0.964156998
## Comp.18 Comp.19 Comp.20 Comp.21
## Standard deviation 0.554937996 0.536514703 0.489180764 0.452942826
## Proportion of Variance 0.004052055 0.003787474 0.003148656 0.002699437
## Cumulative Proportion 0.968209053 0.971996527 0.975145183 0.977844620
## Comp.22 Comp.23 Comp.24 Comp.25
## Standard deviation 0.413036486 0.371984607 0.345332244 0.340925995
## Proportion of Variance 0.002244726 0.001820691 0.001569136 0.001529349
## Cumulative Proportion 0.980089345 0.981910037 0.983479173 0.985008522
## Comp.26 Comp.27 Comp.28 Comp.29
## Standard deviation 0.315955870 0.3111900 0.290415031 0.2684645335
## Proportion of Variance 0.001313528 0.0012742 0.001109749 0.0009483317
## Cumulative Proportion 0.986322050 0.9875962 0.988705998 0.9896543300
## Comp.30 Comp.31 Comp.32 Comp.33
## Standard deviation 0.2604588689 0.2531467576 0.2421615073 0.2320105035
## Proportion of Variance 0.0008926161 0.0008432011 0.0007716078 0.0007082747
## Cumulative Proportion 0.9905469460 0.9913901471 0.9921617549 0.9928700296
## Comp.34 Comp.35 Comp.36 Comp.37
## Standard deviation 0.2179406924 0.2005000901 0.1992667450 0.1870008394
## Proportion of Variance 0.0006249756 0.0005289511 0.0005224636 0.0004601226
## Cumulative Proportion 0.9934950052 0.9940239563 0.9945464200 0.9950065425
## Comp.38 Comp.39 Comp.40 Comp.41
## Standard deviation 0.1801746263 0.1764957207 0.1678065497 0.1555696714
## Proportion of Variance 0.0004271434 0.0004098782 0.0003705137 0.0003184464
## Cumulative Proportion 0.9954336859 0.9958435640 0.9962140777 0.9965325240
## Comp.42 Comp.43 Comp.44 Comp.45
## Standard deviation 0.1539163970 0.1450082065 0.1382741323 0.136004342
## Proportion of Variance 0.0003117139 0.0002766761 0.0002515755 0.000243384
## Cumulative Proportion 0.9968442379 0.9971209140 0.9973724895 0.997615873
## Comp.46 Comp.47 Comp.48 Comp.49
## Standard deviation 0.1295787497 0.1269559002 0.1136970759 0.1104921747
## Proportion of Variance 0.0002209296 0.0002120763 0.0001700924 0.0001606384
## Cumulative Proportion 0.9978368031 0.9980488794 0.9982189718 0.9983796103
## Comp.50 Comp.51 Comp.52 Comp.53
## Standard deviation 0.1092435608 0.1028871606 0.1013361821 0.0972856541
## Proportion of Variance 0.0001570284 0.0001392864 0.0001351187 0.0001245329
## Cumulative Proportion 0.9985366386 0.9986759250 0.9988110437 0.9989355766
## Comp.54 Comp.55 Comp.56 Comp.57
## Standard deviation 0.0883929728 8.525294e-02 8.334805e-02 8.101791e-02
## Proportion of Variance 0.0001028068 9.563242e-05 9.140654e-05 8.636713e-05
## Cumulative Proportion 0.9990383834 9.991340e-01 9.992254e-01 9.993118e-01
## Comp.58 Comp.59 Comp.60 Comp.61
## Standard deviation 7.776973e-02 0.0714461190 6.606618e-02 6.423756e-02
## Proportion of Variance 7.958066e-05 0.0000671651 5.743078e-05 5.429557e-05
## Cumulative Proportion 9.993914e-01 0.9994585353 9.995160e-01 9.995703e-01
## Comp.62 Comp.63 Comp.64 Comp.65
## Standard deviation 0.0623595609 6.051724e-02 5.985591e-02 5.678850e-02
## Proportion of Variance 0.0000511673 4.818863e-05 4.714118e-05 4.243334e-05
## Cumulative Proportion 0.9996214289 9.996696e-01 9.997168e-01 9.997592e-01
## Comp.66 Comp.67 Comp.68 Comp.69
## Standard deviation 5.326286e-02 4.790068e-02 4.656519e-02 4.552167e-02
## Proportion of Variance 3.732805e-05 3.019047e-05 2.853049e-05 2.726609e-05
## Cumulative Proportion 9.997965e-01 9.998267e-01 9.998552e-01 9.998825e-01
## Comp.70 Comp.71 Comp.72 Comp.73
## Standard deviation 4.205543e-02 3.995160e-02 3.848784e-02 3.558922e-02
## Proportion of Variance 2.327183e-05 2.100171e-05 1.949098e-05 1.666569e-05
## Cumulative Proportion 9.999058e-01 9.999268e-01 9.999463e-01 9.999629e-01
## Comp.74 Comp.75 Comp.76
## Standard deviation 3.385418e-02 3.072409e-02 2.695704e-02
## Proportion of Variance 1.508033e-05 1.242065e-05 9.561608e-06
## Cumulative Proportion 9.999780e-01 9.999904e-01 1.000000e+00plot(uk.floods.pca.5,type = "l")
biplot(uk.floods.pca.5)
The same analysis after standarization of the data yields:
uk.floods.phi.1.scaled <- scale(uk.floods.phi.1)
uk.floods.phi.2.scaled <- scale(uk.floods.phi.2)
uk.floods.phi.3.scaled <- scale(uk.floods.phi.3)
uk.floods.phi.4.scaled <- scale(uk.floods.phi.4)
uk.floods.phi.5.scaled <- scale(uk.floods.phi.5)
colMeans(uk.floods.phi.1.scaled) # faster version of apply(scaled.dat, 2, mean)## [1] -1.497930e-15 1.288421e-15 -9.126160e-16 5.290562e-16 -1.110319e-15
## [6] -1.034666e-15 1.327174e-15 1.205055e-15 1.586584e-16 -5.396986e-16
## [11] -8.948970e-20 -7.663520e-16 1.472188e-15 2.276549e-15 -2.209707e-18
## [16] -2.669960e-16 -2.867894e-15 -1.507640e-15 -1.097984e-15 -1.515412e-15
## [21] 8.691171e-17 -1.101121e-15 -1.721176e-15 -1.935573e-15 -1.231898e-15
## [26] -9.321729e-17 2.827511e-15 2.414329e-15 -8.677541e-16 2.015283e-15
## [31] 7.783539e-17 6.529341e-16 1.444501e-16 -1.038810e-15 -1.789846e-15
## [36] -1.909411e-15 2.311519e-15 -8.543788e-16 -1.544785e-15 1.656950e-15
## [41] 7.043390e-16 1.950834e-15 -5.826933e-16 -1.734211e-15 6.701266e-16
## [46] 2.480369e-15 -2.491023e-16 -2.706823e-16 1.087806e-15 -1.121258e-15
## [51] -1.056658e-16 -2.835337e-15 1.832274e-15 9.229194e-16 -1.038612e-15
## [56] -6.401956e-19 -1.410588e-15 1.232232e-15 -1.952755e-15 5.706139e-16
## [61] -1.575115e-15 -2.040572e-15 -7.092403e-17 2.345522e-15apply(uk.floods.phi.1.scaled, 2, sd)## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [36] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1uk.floods.pca.1.scaled <- princomp(uk.floods.phi.1.scaled , cor = TRUE, scores = TRUE)
uk.floods.pca.2.scaled <- princomp(uk.floods.phi.2.scaled , cor = TRUE, scores = TRUE)
uk.floods.pca.3.scaled <- princomp(uk.floods.phi.3.scaled , cor = TRUE, scores = TRUE)
uk.floods.pca.4.scaled <- princomp(uk.floods.phi.4.scaled , cor = TRUE, scores = TRUE)
uk.floods.pca.5.scaled <- princomp(uk.floods.phi.5.scaled , cor = TRUE, scores = TRUE)
summary(uk.floods.pca.1.scaled)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 5.5428126 2.9515918 2.48046518 1.82251017
## Proportion of Variance 0.4800433 0.1361233 0.09613605 0.05189911
## Cumulative Proportion 0.4800433 0.6161666 0.71230270 0.76420181
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 1.72472263 1.34675032 1.2858591 1.16932601
## Proportion of Variance 0.04647919 0.02833963 0.0258349 0.02136443
## Cumulative Proportion 0.81068100 0.83902064 0.8648555 0.88621996
## Comp.9 Comp.10 Comp.11 Comp.12
## Standard deviation 1.03778324 0.97687798 0.88555546 0.83398758
## Proportion of Variance 0.01682803 0.01491079 0.01225326 0.01086774
## Cumulative Proportion 0.90304799 0.91795878 0.93021204 0.94107978
## Comp.13 Comp.14 Comp.15 Comp.16
## Standard deviation 0.793749748 0.626746517 0.573708158 0.524433517
## Proportion of Variance 0.009844354 0.006137675 0.005142829 0.004297352
## Cumulative Proportion 0.950924135 0.957061810 0.962204639 0.966501990
## Comp.17 Comp.18 Comp.19 Comp.20
## Standard deviation 0.494338471 0.467170644 0.435385818 0.412190488
## Proportion of Variance 0.003818289 0.003410131 0.002961888 0.002654703
## Cumulative Proportion 0.970320280 0.973730411 0.976692299 0.979347002
## Comp.21 Comp.22 Comp.23 Comp.24
## Standard deviation 0.3812821 0.337125897 0.333472773 0.307186937
## Proportion of Variance 0.0022715 0.001775842 0.001737564 0.001474435
## Cumulative Proportion 0.9816185 0.983394344 0.985131908 0.986606342
## Comp.25 Comp.26 Comp.27 Comp.28
## Standard deviation 0.299800148 0.279972984 0.263207732 0.2478024447
## Proportion of Variance 0.001404377 0.001224764 0.001082474 0.0009594696
## Cumulative Proportion 0.988010719 0.989235483 0.990317957 0.9912774261
## Comp.29 Comp.30 Comp.31 Comp.32
## Standard deviation 0.2354442700 0.2269615887 0.2136297658 0.2038270777
## Proportion of Variance 0.0008661563 0.0008048682 0.0007130887 0.0006491481
## Cumulative Proportion 0.9921435824 0.9929484506 0.9936615393 0.9943106874
## Comp.33 Comp.34 Comp.35 Comp.36
## Standard deviation 0.1812106128 0.1779718986 0.1686612915 0.1664002714
## Proportion of Variance 0.0005130826 0.0004949062 0.0004444786 0.0004326414
## Cumulative Proportion 0.9948237700 0.9953186762 0.9957631548 0.9961957962
## Comp.37 Comp.38 Comp.39 Comp.40
## Standard deviation 0.1540856670 0.149071141 0.1392531748 0.1299883254
## Proportion of Variance 0.0003709749 0.000347222 0.0003029914 0.0002640151
## Cumulative Proportion 0.9965667711 0.996913993 0.9972169844 0.9974809995
## Comp.41 Comp.42 Comp.43 Comp.44
## Standard deviation 0.1269949048 0.1227905374 0.1148577325 0.1111628327
## Proportion of Variance 0.0002519954 0.0002355862 0.0002061297 0.0001930809
## Cumulative Proportion 0.9977329949 0.9979685811 0.9981747107 0.9983677916
## Comp.45 Comp.46 Comp.47 Comp.48
## Standard deviation 0.1058692382 0.1026929396 0.0967983997 0.0959115396
## Proportion of Variance 0.0001751296 0.0001647787 0.0001464052 0.0001437347
## Cumulative Proportion 0.9985429212 0.9987077000 0.9988541051 0.9989978399
## Comp.49 Comp.50 Comp.51 Comp.52
## Standard deviation 0.086068640 0.0851839751 7.896836e-02 7.612013e-02
## Proportion of Variance 0.000115747 0.0001133798 9.743754e-05 9.053553e-05
## Cumulative Proportion 0.999113587 0.9992269667 9.993244e-01 9.994149e-01
## Comp.53 Comp.54 Comp.55 Comp.56
## Standard deviation 7.224699e-02 6.711442e-02 6.429725e-02 6.041894e-02
## Proportion of Variance 8.155668e-05 7.038039e-05 6.459587e-05 5.703826e-05
## Cumulative Proportion 9.994965e-01 9.995669e-01 9.996315e-01 9.996885e-01
## Comp.57 Comp.58 Comp.59 Comp.60
## Standard deviation 5.883503e-02 5.714398e-02 5.446225e-02 5.186803e-02
## Proportion of Variance 5.408688e-05 5.102241e-05 4.634588e-05 4.203583e-05
## Cumulative Proportion 9.997426e-01 9.997936e-01 9.998400e-01 9.998820e-01
## Comp.61 Comp.62 Comp.63 Comp.64
## Standard deviation 4.943895e-02 4.550653e-02 0.0405321416 3.733581e-02
## Proportion of Variance 3.819078e-05 3.235694e-05 0.0000256696 2.178066e-05
## Cumulative Proportion 9.999202e-01 9.999525e-01 0.9999782193 1.000000e+00plot(uk.floods.pca.1.scaled,type = "l")
biplot(uk.floods.pca.1.scaled)
summary(uk.floods.pca.2.scaled)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 5.7914986 2.5766337 2.03315372 1.68693923
## Proportion of Variance 0.5324041 0.1053816 0.06561451 0.04517086
## Cumulative Proportion 0.5324041 0.6377857 0.70340018 0.74857103
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 1.55516019 1.45535431 1.31504182 1.18106522
## Proportion of Variance 0.03838926 0.03361994 0.02744976 0.02214151
## Cumulative Proportion 0.78696029 0.82058023 0.84802999 0.87017150
## Comp.9 Comp.10 Comp.11 Comp.12
## Standard deviation 1.13926441 1.10797992 0.9446200 0.8662195
## Proportion of Variance 0.02060196 0.01948602 0.0141636 0.0119101
## Cumulative Proportion 0.89077346 0.91025948 0.9244231 0.9363332
## Comp.13 Comp.14 Comp.15 Comp.16
## Standard deviation 0.672704884 0.647042660 0.599396769 0.56264156
## Proportion of Variance 0.007183045 0.006645464 0.005702801 0.00502485
## Cumulative Proportion 0.943516229 0.950161693 0.955864494 0.96088934
## Comp.17 Comp.18 Comp.19 Comp.20
## Standard deviation 0.534804998 0.509096026 0.479531260 0.434310933
## Proportion of Variance 0.004539943 0.004113949 0.003650004 0.002994063
## Cumulative Proportion 0.965429286 0.969543235 0.973193239 0.976187302
## Comp.21 Comp.22 Comp.23 Comp.24
## Standard deviation 0.429494503 0.399321329 0.385714730 0.344945671
## Proportion of Variance 0.002928024 0.002531072 0.002361521 0.001888691
## Cumulative Proportion 0.979115326 0.981646398 0.984007920 0.985896610
## Comp.25 Comp.26 Comp.27 Comp.28
## Standard deviation 0.307808131 0.287796038 0.271133216 0.268433130
## Proportion of Variance 0.001503902 0.001314707 0.001166877 0.001143752
## Cumulative Proportion 0.987400513 0.988715220 0.989882096 0.991025848
## Comp.29 Comp.30 Comp.31 Comp.32
## Standard deviation 0.244780718 0.2378794578 0.220259586 0.2072855330
## Proportion of Variance 0.000951073 0.0008982006 0.000770068 0.0006820205
## Cumulative Proportion 0.991976921 0.9928751215 0.993645190 0.9943272100
## Comp.33 Comp.34 Comp.35 Comp.36
## Standard deviation 0.1849073918 0.1727819699 0.1711256422 0.1551283133
## Proportion of Variance 0.0005427102 0.0004738668 0.0004648252 0.0003819809
## Cumulative Proportion 0.9948699203 0.9953437871 0.9958086122 0.9961905931
## Comp.37 Comp.38 Comp.39 Comp.40
## Standard deviation 0.1514736283 0.1457754718 0.1425389311 0.1362243222
## Proportion of Variance 0.0003641946 0.0003373093 0.0003224976 0.0002945566
## Cumulative Proportion 0.9965547877 0.9968920970 0.9972145946 0.9975091512
## Comp.41 Comp.42 Comp.43 Comp.44
## Standard deviation 0.1271351193 0.1256545841 0.1179316034 0.1115743787
## Proportion of Variance 0.0002565609 0.0002506202 0.0002207597 0.0001976007
## Cumulative Proportion 0.9977657121 0.9980163324 0.9982370921 0.9984346928
## Comp.45 Comp.46 Comp.47 Comp.48
## Standard deviation 0.106734975 0.1004459134 0.0967299238 0.0952466223
## Proportion of Variance 0.000180831 0.0001601489 0.0001485187 0.0001439987
## Cumulative Proportion 0.998615524 0.9987756727 0.9989241914 0.9990681901
## Comp.49 Comp.50 Comp.51 Comp.52
## Standard deviation 0.0880635999 0.0838067008 0.0803390640 7.748467e-02
## Proportion of Variance 0.0001230984 0.0001114851 0.0001024502 9.529959e-05
## Cumulative Proportion 0.9991912885 0.9993027736 0.9994052239 9.995005e-01
## Comp.53 Comp.54 Comp.55 Comp.56
## Standard deviation 6.873348e-02 0.063771771 5.972640e-02 5.899985e-02
## Proportion of Variance 7.498875e-05 0.000064553 5.662291e-05 5.525368e-05
## Cumulative Proportion 9.995755e-01 0.999640065 9.996967e-01 9.997519e-01
## Comp.57 Comp.58 Comp.59 Comp.60
## Standard deviation 5.587238e-02 5.239672e-02 5.083849e-02 4.678487e-02
## Proportion of Variance 4.955116e-05 4.357803e-05 4.102463e-05 3.474325e-05
## Cumulative Proportion 9.998015e-01 9.998451e-01 9.998861e-01 9.999208e-01
## Comp.61 Comp.62 Comp.63
## Standard deviation 4.334473e-02 0.0419344749 3.674080e-02
## Proportion of Variance 2.982168e-05 0.0000279127 2.142677e-05
## Cumulative Proportion 9.999507e-01 0.9999785732 1.000000e+00plot(uk.floods.pca.2.scaled,type = "l")
biplot(uk.floods.pca.2.scaled)
summary(uk.floods.pca.3.scaled)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 5.2938692 2.6580452 2.25340883 2.02650892
## Proportion of Variance 0.4520169 0.1139549 0.08190083 0.06623772
## Cumulative Proportion 0.4520169 0.5659719 0.64787268 0.71411040
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 1.67438048 1.56755744 1.37654757 1.28550769
## Proportion of Variance 0.04521855 0.03963284 0.03056263 0.02665371
## Cumulative Proportion 0.75932895 0.79896179 0.82952442 0.85617813
## Comp.9 Comp.10 Comp.11 Comp.12
## Standard deviation 1.20545766 1.15035126 0.93005447 0.85195612
## Proportion of Variance 0.02343755 0.02134368 0.01395163 0.01170692
## Cumulative Proportion 0.87961568 0.90095936 0.91491100 0.92661792
## Comp.13 Comp.14 Comp.15 Comp.16
## Standard deviation 0.741437580 0.679919411 0.651188725 0.644603034
## Proportion of Variance 0.008866608 0.007456297 0.006839464 0.006701824
## Cumulative Proportion 0.935484528 0.942940824 0.949780288 0.956482112
## Comp.17 Comp.18 Comp.19 Comp.20
## Standard deviation 0.584597568 0.538380162 0.499047712 0.481103591
## Proportion of Variance 0.005512166 0.004675052 0.004016913 0.003733237
## Cumulative Proportion 0.961994278 0.966669330 0.970686243 0.974419480
## Comp.21 Comp.22 Comp.23 Comp.24
## Standard deviation 0.423923375 0.409626402 0.362209281 0.35062511
## Proportion of Variance 0.002898565 0.002706351 0.002116057 0.00198287
## Cumulative Proportion 0.977318045 0.980024396 0.982140454 0.98412332
## Comp.25 Comp.26 Comp.27 Comp.28
## Standard deviation 0.314139557 0.298218180 0.292358284 0.275495982
## Proportion of Variance 0.001591672 0.001434421 0.001378603 0.001224162
## Cumulative Proportion 0.985714996 0.987149417 0.988528019 0.989752181
## Comp.29 Comp.30 Comp.31 Comp.32
## Standard deviation 0.265092498 0.252704834 0.2328552340 0.2261129049
## Proportion of Variance 0.001133452 0.001029996 0.0008745413 0.0008246298
## Cumulative Proportion 0.990885633 0.991915629 0.9927901704 0.9936148002
## Comp.33 Comp.34 Comp.35 Comp.36
## Standard deviation 0.1942658611 0.1795607865 0.1724554016 0.1658891648
## Proportion of Variance 0.0006086972 0.0005200335 0.0004796914 0.0004438583
## Cumulative Proportion 0.9942234973 0.9947435308 0.9952232222 0.9956670805
## Comp.37 Comp.38 Comp.39 Comp.40
## Standard deviation 0.1607241976 0.1572177236 0.1510054183 0.1465683292
## Proportion of Variance 0.0004166495 0.0003986679 0.0003677845 0.0003464883
## Cumulative Proportion 0.9960837300 0.9964823979 0.9968501824 0.9971966707
## Comp.41 Comp.42 Comp.43 Comp.44
## Standard deviation 0.1418071591 0.1365331380 0.1246291368 0.1140609925
## Proportion of Variance 0.0003243431 0.0003006661 0.0002505229 0.0002098373
## Cumulative Proportion 0.9975210138 0.9978216799 0.9980722028 0.9982820400
## Comp.45 Comp.46 Comp.47 Comp.48
## Standard deviation 0.1071221862 0.1023465376 0.0981430711 0.0961575403
## Proportion of Variance 0.0001850833 0.0001689486 0.0001553558 0.0001491334
## Cumulative Proportion 0.9984671233 0.9986360719 0.9987914278 0.9989405612
## Comp.49 Comp.50 Comp.51 Comp.52
## Standard deviation 0.0936399679 0.0864824739 0.08435851 0.0810879961
## Proportion of Variance 0.0001414265 0.0001206326 0.00011478 0.0001060526
## Cumulative Proportion 0.9990819877 0.9992026203 0.99931740 0.9994234529
## Comp.53 Comp.54 Comp.55 Comp.56
## Standard deviation 0.0760095490 7.571987e-02 7.126708e-02 0.0644860568
## Proportion of Variance 0.0000931847 9.247579e-05 8.191931e-05 0.0000670718
## Cumulative Proportion 0.9995166376 9.996091e-01 9.996910e-01 0.9997581045
## Comp.57 Comp.58 Comp.59 Comp.60
## Standard deviation 6.257980e-02 5.481935e-02 4.892527e-02 4.664822e-02
## Proportion of Variance 6.316501e-05 4.847035e-05 3.860778e-05 3.509768e-05
## Cumulative Proportion 9.998213e-01 9.998697e-01 9.999083e-01 9.999434e-01
## Comp.61 Comp.62
## Standard deviation 4.245669e-02 0.041277379
## Proportion of Variance 2.907372e-05 0.000027481
## Cumulative Proportion 9.999725e-01 1.000000000plot(uk.floods.pca.3.scaled,type = "l")
biplot(uk.floods.pca.3.scaled)
summary(uk.floods.pca.4.scaled)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 4.7869281 3.1080861 2.7410716 2.19377798 1.98965968
## Proportion of Variance 0.3637251 0.1533365 0.1192615 0.07639146 0.06283723
## Cumulative Proportion 0.3637251 0.5170616 0.6363231 0.71271453 0.77555176
## Comp.6 Comp.7 Comp.8 Comp.9
## Standard deviation 1.69507822 1.56778212 1.16863526 1.09341065
## Proportion of Variance 0.04560778 0.03901493 0.02167791 0.01897693
## Cumulative Proportion 0.82115954 0.86017447 0.88185238 0.90082932
## Comp.10 Comp.11 Comp.12 Comp.13
## Standard deviation 0.97608289 0.86254198 0.770816241 0.71321559
## Proportion of Variance 0.01512282 0.01180919 0.009431074 0.00807423
## Cumulative Proportion 0.91595214 0.92776132 0.937192399 0.94526663
## Comp.14 Comp.15 Comp.16 Comp.17
## Standard deviation 0.662687770 0.622374403 0.593903068 0.538138908
## Proportion of Variance 0.006970716 0.006148411 0.005598744 0.004596722
## Cumulative Proportion 0.952237344 0.958385756 0.963984499 0.968581221
## Comp.18 Comp.19 Comp.20 Comp.21
## Standard deviation 0.523684033 0.420935441 0.414724004 0.389568484
## Proportion of Variance 0.004353095 0.002812486 0.002730095 0.002408946
## Cumulative Proportion 0.972934316 0.975746802 0.978476898 0.980885844
## Comp.22 Comp.23 Comp.24 Comp.25
## Standard deviation 0.351435583 0.334014483 0.31105329 0.303903045
## Proportion of Variance 0.001960428 0.001770884 0.00153578 0.001465985
## Cumulative Proportion 0.982846272 0.984617156 0.98615294 0.987618921
## Comp.26 Comp.27 Comp.28 Comp.29
## Standard deviation 0.288710201 0.268304049 0.2473686122 0.2428001108
## Proportion of Variance 0.001323073 0.001142652 0.0009712894 0.0009357443
## Cumulative Proportion 0.988941993 0.990084645 0.9910559346 0.9919916790
## Comp.30 Comp.31 Comp.32 Comp.33
## Standard deviation 0.2227578186 0.2056951515 0.2035116813 0.1896102211
## Proportion of Variance 0.0007876356 0.0006715952 0.0006574128 0.0005706672
## Cumulative Proportion 0.9927793146 0.9934509098 0.9941083226 0.9946789898
## Comp.34 Comp.35 Comp.36 Comp.37
## Standard deviation 0.1788091235 0.1732990919 0.1635975222 0.1578360999
## Proportion of Variance 0.0005075032 0.0004767075 0.0004248278 0.0003954323
## Cumulative Proportion 0.9951864930 0.9956632006 0.9960880283 0.9964834606
## Comp.38 Comp.39 Comp.40 Comp.41
## Standard deviation 0.1510721125 0.1353475422 0.1338550089 0.1255108249
## Proportion of Variance 0.0003622664 0.0002907771 0.0002843994 0.0002500471
## Cumulative Proportion 0.9968457270 0.9971365041 0.9974209035 0.9976709506
## Comp.42 Comp.43 Comp.44 Comp.45
## Standard deviation 0.1193761716 0.1162381718 0.1150479880 0.1066346176
## Proportion of Variance 0.0002262011 0.0002144653 0.0002100959 0.0001804911
## Cumulative Proportion 0.9978971518 0.9981116170 0.9983217129 0.9985022040
## Comp.46 Comp.47 Comp.48 Comp.49
## Standard deviation 0.1006978758 0.0988381641 0.0937515086 0.091193835
## Proportion of Variance 0.0001609534 0.0001550632 0.0001395134 0.000132005
## Cumulative Proportion 0.9986631574 0.9988182206 0.9989577340 0.999089739
## Comp.50 Comp.51 Comp.52 Comp.53
## Standard deviation 0.0874813180 0.0824329058 0.07918977 7.687006e-02
## Proportion of Variance 0.0001214759 0.0001078601 0.00009954 9.379376e-05
## Cumulative Proportion 0.9992112149 0.9993190750 0.99941862 9.995124e-01
## Comp.54 Comp.55 Comp.56 Comp.57
## Standard deviation 6.894398e-02 6.681377e-02 6.445607e-02 6.138645e-02
## Proportion of Variance 7.544878e-05 7.085841e-05 6.594579e-05 5.981422e-05
## Cumulative Proportion 9.995879e-01 9.996587e-01 9.997247e-01 9.997845e-01
## Comp.58 Comp.59 Comp.60 Comp.61
## Standard deviation 5.706758e-02 5.158880e-02 4.604085e-02 4.480615e-02
## Proportion of Variance 5.169378e-05 4.224451e-05 3.364698e-05 3.186652e-05
## Cumulative Proportion 9.998362e-01 9.998784e-01 9.999121e-01 9.999439e-01
## Comp.62 Comp.63
## Standard deviation 4.385092e-02 4.012042e-02
## Proportion of Variance 3.052228e-05 2.554997e-05
## Cumulative Proportion 9.999745e-01 1.000000e+00plot(uk.floods.pca.4.scaled,type = "l")
biplot(uk.floods.pca.4.scaled)
summary(uk.floods.pca.5.scaled)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 5.5246005 3.3717505 2.8793219 2.34074667 2.07905339
## Proportion of Variance 0.4015949 0.1495882 0.1090855 0.07209336 0.05687451
## Cumulative Proportion 0.4015949 0.5511831 0.6602685 0.73236187 0.78923639
## Comp.6 Comp.7 Comp.8 Comp.9
## Standard deviation 1.65068186 1.46332986 1.30396168 1.20054850
## Proportion of Variance 0.03585198 0.02817545 0.02237258 0.01896469
## Cumulative Proportion 0.82508837 0.85326382 0.87563640 0.89460109
## Comp.10 Comp.11 Comp.12 Comp.13
## Standard deviation 1.0777961 0.93388575 0.88641449 0.84324408
## Proportion of Variance 0.0152848 0.01147556 0.01033856 0.00935606
## Cumulative Proportion 0.9098859 0.92136145 0.93170001 0.94105607
## Comp.14 Comp.15 Comp.16 Comp.17
## Standard deviation 0.718511388 0.676440212 0.658449589 0.590156398
## Proportion of Variance 0.006792877 0.006020676 0.005704682 0.004582692
## Cumulative Proportion 0.947848948 0.953869624 0.959574306 0.964156998
## Comp.18 Comp.19 Comp.20 Comp.21
## Standard deviation 0.554937996 0.536514703 0.489180764 0.452942826
## Proportion of Variance 0.004052055 0.003787474 0.003148656 0.002699437
## Cumulative Proportion 0.968209053 0.971996527 0.975145183 0.977844620
## Comp.22 Comp.23 Comp.24 Comp.25
## Standard deviation 0.413036486 0.371984607 0.345332244 0.340925995
## Proportion of Variance 0.002244726 0.001820691 0.001569136 0.001529349
## Cumulative Proportion 0.980089345 0.981910037 0.983479173 0.985008522
## Comp.26 Comp.27 Comp.28 Comp.29
## Standard deviation 0.315955870 0.3111900 0.290415031 0.2684645335
## Proportion of Variance 0.001313528 0.0012742 0.001109749 0.0009483317
## Cumulative Proportion 0.986322050 0.9875962 0.988705998 0.9896543300
## Comp.30 Comp.31 Comp.32 Comp.33
## Standard deviation 0.2604588689 0.2531467576 0.2421615073 0.2320105035
## Proportion of Variance 0.0008926161 0.0008432011 0.0007716078 0.0007082747
## Cumulative Proportion 0.9905469460 0.9913901471 0.9921617549 0.9928700296
## Comp.34 Comp.35 Comp.36 Comp.37
## Standard deviation 0.2179406924 0.2005000901 0.1992667450 0.1870008394
## Proportion of Variance 0.0006249756 0.0005289511 0.0005224636 0.0004601226
## Cumulative Proportion 0.9934950052 0.9940239563 0.9945464200 0.9950065425
## Comp.38 Comp.39 Comp.40 Comp.41
## Standard deviation 0.1801746263 0.1764957207 0.1678065497 0.1555696714
## Proportion of Variance 0.0004271434 0.0004098782 0.0003705137 0.0003184464
## Cumulative Proportion 0.9954336859 0.9958435640 0.9962140777 0.9965325240
## Comp.42 Comp.43 Comp.44 Comp.45
## Standard deviation 0.1539163970 0.1450082065 0.1382741323 0.136004342
## Proportion of Variance 0.0003117139 0.0002766761 0.0002515755 0.000243384
## Cumulative Proportion 0.9968442379 0.9971209140 0.9973724895 0.997615873
## Comp.46 Comp.47 Comp.48 Comp.49
## Standard deviation 0.1295787497 0.1269559002 0.1136970759 0.1104921747
## Proportion of Variance 0.0002209296 0.0002120763 0.0001700924 0.0001606384
## Cumulative Proportion 0.9978368031 0.9980488794 0.9982189718 0.9983796103
## Comp.50 Comp.51 Comp.52 Comp.53
## Standard deviation 0.1092435608 0.1028871606 0.1013361821 0.0972856541
## Proportion of Variance 0.0001570284 0.0001392864 0.0001351187 0.0001245329
## Cumulative Proportion 0.9985366386 0.9986759250 0.9988110437 0.9989355766
## Comp.54 Comp.55 Comp.56 Comp.57
## Standard deviation 0.0883929728 8.525294e-02 8.334805e-02 8.101791e-02
## Proportion of Variance 0.0001028068 9.563242e-05 9.140654e-05 8.636713e-05
## Cumulative Proportion 0.9990383834 9.991340e-01 9.992254e-01 9.993118e-01
## Comp.58 Comp.59 Comp.60 Comp.61
## Standard deviation 7.776973e-02 0.0714461190 6.606618e-02 6.423756e-02
## Proportion of Variance 7.958066e-05 0.0000671651 5.743078e-05 5.429557e-05
## Cumulative Proportion 9.993914e-01 0.9994585353 9.995160e-01 9.995703e-01
## Comp.62 Comp.63 Comp.64 Comp.65
## Standard deviation 0.0623595609 6.051724e-02 5.985591e-02 5.678850e-02
## Proportion of Variance 0.0000511673 4.818863e-05 4.714118e-05 4.243334e-05
## Cumulative Proportion 0.9996214289 9.996696e-01 9.997168e-01 9.997592e-01
## Comp.66 Comp.67 Comp.68 Comp.69
## Standard deviation 5.326286e-02 4.790068e-02 4.656519e-02 4.552167e-02
## Proportion of Variance 3.732805e-05 3.019047e-05 2.853049e-05 2.726609e-05
## Cumulative Proportion 9.997965e-01 9.998267e-01 9.998552e-01 9.998825e-01
## Comp.70 Comp.71 Comp.72 Comp.73
## Standard deviation 4.205543e-02 3.995160e-02 3.848784e-02 3.558922e-02
## Proportion of Variance 2.327183e-05 2.100171e-05 1.949098e-05 1.666569e-05
## Cumulative Proportion 9.999058e-01 9.999268e-01 9.999463e-01 9.999629e-01
## Comp.74 Comp.75 Comp.76
## Standard deviation 3.385418e-02 3.072409e-02 2.695704e-02
## Proportion of Variance 1.508033e-05 1.242065e-05 9.561608e-06
## Cumulative Proportion 9.999780e-01 9.999904e-01 1.000000e+00plot(uk.floods.pca.5.scaled,type = "l")
biplot(uk.floods.pca.5.scaled)